The potential for automated UI tests to become slow and unreliable lies in the excessive use of Selenium commands. A case study demonstrates how optimizing a test by addressing inefficient Selenium command usage can significantly improve its speed, reducing execution time from 95 seconds to 17 seconds, a 560% increase in performance. By identifying and eliminating unnecessary web requests and actions, such as validating element states after each click, the refactored test executes only essential commands, resulting in faster and more reliable tests.